Singular surfaces, mod 2 homology, and hyperbolic volume, I

Authors:
Ian Agol, Marc Culler and Peter B. Shalen

Journal:
Trans. Amer. Math. Soc. **362** (2010), 3463-3498

MSC (2000):
Primary 57M50

DOI:
https://doi.org/10.1090/S0002-9947-10-04362-X

Published electronically:
February 2, 2010

MathSciNet review:
2601597

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a simple, closed, orientable -manifold such that contains a genus- surface group, and if has rank at least , we show that contains an embedded closed incompressible surface of genus at most . As an application we show that if is a closed orientable hyperbolic -manifold of volume at most , then the rank of is at most .

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Additional Information

**Ian Agol**

Affiliation:
Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, California 94720-3840

Email:
ianagol@math.berkeley.edu

**Marc Culler**

Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607-7045

Email:
culler@math.uic.edu

**Peter B. Shalen**

Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607-7045

Email:
shalen@math.uic.edu

DOI:
https://doi.org/10.1090/S0002-9947-10-04362-X

Received by editor(s):
July 3, 2005

Received by editor(s) in revised form:
February 2, 2008

Published electronically:
February 2, 2010

Additional Notes:
This work was partially supported by NSF grants DMS-0204142 and DMS-0504975

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.